Lesson 8.2: Comparing Boundaries and Real-World Fencing Problems
Compare perimeters of different geometric layouts, solve missing side puzzles, and plan real-world borders.
⏱️ Reading Time: 15 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Perimeter and Measuring Boundaries
An interior decorator frames artwork. A square painting has 20 cm sides (P = 80 cm), while a long rectangular panorama is 30 cm by 10 cm (P = 80 cm). Although shapes differ completely, both require identical 80 cm lengths of framing wood.
💡 Core Mathematical Concepts: Comparing Boundaries & Fencing
Focus areas: Perimeter comparison, missing side length, framing, ribbon borders.
| Concept / Term | Mathematical Definition | Everyday Example |
|---|---|---|
| Equal Perimeters, Different Shapes | Shapes with completely different appearances can possess identical perimeters | A 10×10 square and a 15×5 rectangle both have P = 40 cm |
| Finding a Missing Side | Subtract known sides from total perimeter to find the unknown side | If rectangle P = 30 cm and length = 9 cm, width = (30 - 18) ÷ 2 = 6 cm |
| Fencing Problems | Calculating boundary costs by multiplying perimeter by price per meter | 50 m of fence at $6/m = $300 |
| Non-Convex (L-Shaped) Figures | Decomposing compound shapes to verify all horizontal and vertical boundary edges | Horizontal total = sum of stepped horizontal segments |
🔍 Practical Classroom & Everyday Examples
Example 1: Working Backwards from Perimeter
For a square: Side = Perimeter ÷ 4. (If P = 48 cm, Side = 48 ÷ 4 = 12 cm).
Example 2: Opposite Sides in Rectangles
Remember opposite sides are always equal in length.
⚠️ Watch Out! Common Mistakes to Avoid
Common Error: Dividing rectangle perimeter by 4
Correction: Only a square has 4 equal sides! A rectangle has 2 lengths and 2 widths.
Common Error: Counting internal partition lines
Correction: Perimeter includes ONLY outer boundary edges.
🎯 Quick Self-Check Challenge
A rectangle has a perimeter of 40 cm. If its length is 12 cm, what is its width?
Answer & Explanation:
Two lengths = 2 × 12 = 24 cm. Remaining for two widths = 40 - 24 = 16 cm. Width = 16 ÷ 2 = 8 cm.
🎯 Key Learning Takeaways
Master Perimeter and Measuring Boundaries fundamentals.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G3-M-CH08-WS05
A4 • 15 Qs
Perimeter and Measuring Boundaries — Worksheet 5
Side Sums, Boundary Formulas & Fencing Math (Rooftop Terrace Garden)
G3-M-CH08-WS04
A4 • 15 Qs
Perimeter and Measuring Boundaries — Worksheet 4
Side Sums, Boundary Formulas & Fencing Math (Suburban Backyard Lawn)
G3-M-CH08-WS03
A4 • 15 Qs
Perimeter and Measuring Boundaries — Worksheet 3
Side Sums, Boundary Formulas & Fencing Math (Art Gallery Picture Frame)
G3-M-CH08-WS02
A4 • 15 Qs
Perimeter and Measuring Boundaries — Worksheet 2
Side Sums, Boundary Formulas & Fencing Math (Community Herb Garden)
G3-M-CH08-WS01
A4 • 15 Qs
Perimeter and Measuring Boundaries — Worksheet 1
Side Sums, Boundary Formulas & Fencing Math (School Sports Pitch)
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
A rectangular swimming pool is 12 m long and 6 m wide. A 1-metre wide paved walking path surrounds the pool completely on all sides. What is the outer perimeter of the paved path?
A
44 metres
B
36 metres
C
40 metres
D
48 metres
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
44 metres
Step-by-Step Explanation:
Outer length = 12 + 1 + 1 = 14 m. Outer width = 6 + 1 + 1 = 8 m. Outer perimeter = 2 × (14 + 8) = 2 × 22 = 44 metres.
2
Short Answer
Hard
2 Marks
An equilateral triangle and a square have the exact same perimeter of 36 cm. How much longer is a side of the triangle than a side of the square?
A
3 cm longer
B
2 cm longer
C
4 cm longer
D
1 cm longer
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3 cm longer
Step-by-Step Explanation:
Triangle side = 36 ÷ 3 = 12 cm. Square side = 36 ÷ 4 = 9 cm. Difference = 12 - 9 = 3 cm longer.
3
Short Answer
Hard
2 Marks
If you double the side length of a square from 5 cm to 10 cm, what happens to its perimeter?
A
The perimeter exactly doubles from 20 cm to 40 cm
B
The perimeter quadruples to 80 cm
C
The perimeter stays the same
D
The perimeter increases by 5 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The perimeter exactly doubles from 20 cm to 40 cm
Step-by-Step Explanation:
Perimeter = 4 × side. Doubling the side doubles the perimeter: 4 × 5 = 20 cm; 4 × 10 = 40 cm.
4
Short Answer
Hard
2 Marks
Can two completely different rectangles have the exact same perimeter? Explain.
A
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
B
No, each perimeter belongs to only one rectangle
C
Only if both rectangles are squares
D
No, because lengths must match
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
Step-by-Step Explanation:
Different pairs of length and width can sum to the same semi-perimeter (6+4=10 and 8+2=10, both giving P=20 cm).
5
Short Answer
Medium
1 Mark
Tariq measures an L-shaped room and calculates perimeter by only adding the 4 longest outer walls, omitting 2 inner corners. Why is this incorrect?
A
Perimeter must include the length of EVERY single segment along the closed boundary
B
Inner corners do not have length
C
L-shapes do not have perimeters
D
Tariq should have multiplied by 6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Perimeter must include the length of EVERY single segment along the closed boundary
Step-by-Step Explanation:
Perimeter requires summing every segment along the boundary without skipping any edges.
6
Short Answer
Medium
1 Mark
A student calculates the perimeter of a 6 cm by 4 cm rectangle as 24 cm. What did the student do wrong?
A
The student multiplied length × width (calculating area = 24 cm²) instead of adding all 4 sides (Perimeter = 20 cm)
B
The student added 6 + 4 only
C
The calculation is correct
D
Perimeter cannot be calculated
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The student multiplied length × width (calculating area = 24 cm²) instead of adding all 4 sides (Perimeter = 20 cm)
Step-by-Step Explanation:
Perimeter is 2 × (6 + 4) = 20 cm. 6 × 4 = 24 cm² is the area.
7
Fill in the Blanks
Medium
1 Mark
A square has a perimeter of 120 cm. What is the length of ONE side?
A
30 cm
B
28 cm
C
34 cm
D
60 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30 cm
Step-by-Step Explanation:
Side length = 120 ÷ 4 = 30 cm.
8
Fill in the Blanks
Medium
1 Mark
A rectangle has a perimeter of 88 cm. If its length is 30 cm, what is its width?
A
14 cm
B
16 cm
C
13 cm
D
15 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14 cm
Step-by-Step Explanation:
Two lengths = 60 cm. Remaining for 2 widths = 88 - 60 = 28 cm. Width = 14 cm.
9
Short Answer
Medium
1 Mark
A photograph measuring 15 cm by 10 cm is framed with lace ribbon. If lace costs $2 per 10 cm, how much does the lace border cost?
A
$10
B
$8
C
$12
D
$15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$10
Step-by-Step Explanation:
Perimeter = 2 × (15 + 10) = 50 cm. 50 cm ÷ 10 = 5 units. 5 × $2 = $10.
10
Short Answer
Medium
1 Mark
A gardener wants to put wire fencing around a square vegetable patch with side 9 metres. Fencing costs $5 per metre. What will the fencing cost in total?
A
$180
B
$160
C
$200
D
$90
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$180
Step-by-Step Explanation:
Perimeter = 4 × 9 m = 36 m. Cost = 36 × $5 = $180.
11
Short Answer
Medium
1 Mark
At the Rooftop Terrace Garden, an organizer installs a wooden border around the Patio Deck (30 m long and 14 m wide). What is the total length of border required?
A
88 metres
B
82 metres
C
96 metres
D
420 metres
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
88 metres
Step-by-Step Explanation:
Border length = 2 × (30 + 14) = 88 metres.
12
Multiple Choice
Easy
1 Mark
Which unit is appropriate for measuring perimeter?
A
Centimetres (cm) or metres (m)
B
Square centimetres (cm²)
C
Litres (L)
D
Grams (g)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Centimetres (cm) or metres (m)
Step-by-Step Explanation:
Perimeter is a linear distance, measured in linear units like cm, m, or km.
13
Multiple Choice
Easy
1 Mark
A triangle has sides of 8 cm, 11 cm, and 14 cm. What is its perimeter?
A
33 cm
B
30 cm
C
35 cm
D
32 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
33 cm
Step-by-Step Explanation:
8 + 11 + 14 = 33 cm.
14
Multiple Choice
Easy
1 Mark
What is the perimeter of a square with sides of length 30 cm?
A
120 cm
B
115 cm
C
128 cm
D
900 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
120 cm
Step-by-Step Explanation:
Square perimeter = 4 × 30 = 120 cm.
15
Multiple Choice
Easy
1 Mark
Calculate the perimeter of a rectangle with length 30 cm and width 14 cm:
A
88 cm
B
84 cm
C
94 cm
D
420 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
88 cm
Step-by-Step Explanation:
Perimeter = 2 × (30 + 14) = 2 × 44 = 88 cm.
16
Short Answer
Hard
2 Marks
A rectangular swimming pool is 12 m long and 6 m wide. A 1-metre wide paved walking path surrounds the pool completely on all sides. What is the outer perimeter of the paved path?
A
44 metres
B
36 metres
C
40 metres
D
48 metres
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
44 metres
Step-by-Step Explanation:
Outer length = 12 + 1 + 1 = 14 m. Outer width = 6 + 1 + 1 = 8 m. Outer perimeter = 2 × (14 + 8) = 2 × 22 = 44 metres.
17
Short Answer
Hard
2 Marks
An equilateral triangle and a square have the exact same perimeter of 36 cm. How much longer is a side of the triangle than a side of the square?
A
3 cm longer
B
2 cm longer
C
4 cm longer
D
1 cm longer
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3 cm longer
Step-by-Step Explanation:
Triangle side = 36 ÷ 3 = 12 cm. Square side = 36 ÷ 4 = 9 cm. Difference = 12 - 9 = 3 cm longer.
18
Short Answer
Hard
2 Marks
If you double the side length of a square from 5 cm to 10 cm, what happens to its perimeter?
A
The perimeter exactly doubles from 20 cm to 40 cm
B
The perimeter quadruples to 80 cm
C
The perimeter stays the same
D
The perimeter increases by 5 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The perimeter exactly doubles from 20 cm to 40 cm
Step-by-Step Explanation:
Perimeter = 4 × side. Doubling the side doubles the perimeter: 4 × 5 = 20 cm; 4 × 10 = 40 cm.
19
Short Answer
Hard
2 Marks
Can two completely different rectangles have the exact same perimeter? Explain.
A
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
B
No, each perimeter belongs to only one rectangle
C
Only if both rectangles are squares
D
No, because lengths must match
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
Step-by-Step Explanation:
Different pairs of length and width can sum to the same semi-perimeter (6+4=10 and 8+2=10, both giving P=20 cm).
20
Short Answer
Medium
1 Mark
Tariq measures an L-shaped room and calculates perimeter by only adding the 4 longest outer walls, omitting 2 inner corners. Why is this incorrect?
A
Perimeter must include the length of EVERY single segment along the closed boundary
B
Inner corners do not have length
C
L-shapes do not have perimeters
D
Tariq should have multiplied by 6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Perimeter must include the length of EVERY single segment along the closed boundary
Step-by-Step Explanation:
Perimeter requires summing every segment along the boundary without skipping any edges.
21
Short Answer
Medium
1 Mark
A student calculates the perimeter of a 6 cm by 4 cm rectangle as 24 cm. What did the student do wrong?
A
The student multiplied length × width (calculating area = 24 cm²) instead of adding all 4 sides (Perimeter = 20 cm)
B
The student added 6 + 4 only
C
The calculation is correct
D
Perimeter cannot be calculated
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The student multiplied length × width (calculating area = 24 cm²) instead of adding all 4 sides (Perimeter = 20 cm)
Step-by-Step Explanation:
Perimeter is 2 × (6 + 4) = 20 cm. 6 × 4 = 24 cm² is the area.
22
Fill in the Blanks
Medium
1 Mark
A square has a perimeter of 72 cm. What is the length of ONE side?
A
18 cm
B
16 cm
C
22 cm
D
36 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
18 cm
Step-by-Step Explanation:
Side length = 72 ÷ 4 = 18 cm.
23
Fill in the Blanks
Medium
1 Mark
A rectangle has a perimeter of 54 cm. If its length is 18 cm, what is its width?
A
9 cm
B
11 cm
C
8 cm
D
9 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9 cm
Step-by-Step Explanation:
Two lengths = 36 cm. Remaining for 2 widths = 54 - 36 = 18 cm. Width = 9 cm.
24
Short Answer
Medium
1 Mark
A photograph measuring 15 cm by 10 cm is framed with lace ribbon. If lace costs $2 per 10 cm, how much does the lace border cost?
A
$10
B
$8
C
$12
D
$15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$10
Step-by-Step Explanation:
Perimeter = 2 × (15 + 10) = 50 cm. 50 cm ÷ 10 = 5 units. 5 × $2 = $10.
25
Short Answer
Medium
1 Mark
A gardener wants to put wire fencing around a square vegetable patch with side 9 metres. Fencing costs $5 per metre. What will the fencing cost in total?
A
$180
B
$160
C
$200
D
$90
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$180
Step-by-Step Explanation:
Perimeter = 4 × 9 m = 36 m. Cost = 36 × $5 = $180.
26
Short Answer
Medium
1 Mark
At the Suburban Backyard Lawn, an organizer installs a wooden border around the Play Area (18 m long and 9 m wide). What is the total length of border required?
A
54 metres
B
48 metres
C
62 metres
D
162 metres
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
54 metres
Step-by-Step Explanation:
Border length = 2 × (18 + 9) = 54 metres.
27
Multiple Choice
Easy
1 Mark
Which unit is appropriate for measuring perimeter?
A
Centimetres (cm) or metres (m)
B
Square centimetres (cm²)
C
Litres (L)
D
Grams (g)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Centimetres (cm) or metres (m)
Step-by-Step Explanation:
Perimeter is a linear distance, measured in linear units like cm, m, or km.
28
Multiple Choice
Easy
1 Mark
A triangle has sides of 8 cm, 11 cm, and 14 cm. What is its perimeter?
A
33 cm
B
30 cm
C
35 cm
D
32 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
33 cm
Step-by-Step Explanation:
8 + 11 + 14 = 33 cm.
29
Multiple Choice
Easy
1 Mark
What is the perimeter of a square with sides of length 18 cm?
A
72 cm
B
67 cm
C
80 cm
D
324 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
72 cm
Step-by-Step Explanation:
Square perimeter = 4 × 18 = 72 cm.
30
Multiple Choice
Easy
1 Mark
Calculate the perimeter of a rectangle with length 18 cm and width 9 cm:
A
54 cm
B
50 cm
C
60 cm
D
162 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
54 cm
Step-by-Step Explanation:
Perimeter = 2 × (18 + 9) = 2 × 27 = 54 cm.
31
Short Answer
Hard
2 Marks
A rectangular swimming pool is 12 m long and 6 m wide. A 1-metre wide paved walking path surrounds the pool completely on all sides. What is the outer perimeter of the paved path?
A
44 metres
B
36 metres
C
40 metres
D
48 metres
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
44 metres
Step-by-Step Explanation:
Outer length = 12 + 1 + 1 = 14 m. Outer width = 6 + 1 + 1 = 8 m. Outer perimeter = 2 × (14 + 8) = 2 × 22 = 44 metres.
32
Short Answer
Hard
2 Marks
An equilateral triangle and a square have the exact same perimeter of 36 cm. How much longer is a side of the triangle than a side of the square?
A
3 cm longer
B
2 cm longer
C
4 cm longer
D
1 cm longer
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3 cm longer
Step-by-Step Explanation:
Triangle side = 36 ÷ 3 = 12 cm. Square side = 36 ÷ 4 = 9 cm. Difference = 12 - 9 = 3 cm longer.
33
Short Answer
Hard
2 Marks
If you double the side length of a square from 5 cm to 10 cm, what happens to its perimeter?
A
The perimeter exactly doubles from 20 cm to 40 cm
B
The perimeter quadruples to 80 cm
C
The perimeter stays the same
D
The perimeter increases by 5 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The perimeter exactly doubles from 20 cm to 40 cm
Step-by-Step Explanation:
Perimeter = 4 × side. Doubling the side doubles the perimeter: 4 × 5 = 20 cm; 4 × 10 = 40 cm.
34
Short Answer
Hard
2 Marks
Can two completely different rectangles have the exact same perimeter? Explain.
A
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
B
No, each perimeter belongs to only one rectangle
C
Only if both rectangles are squares
D
No, because lengths must match
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
Step-by-Step Explanation:
Different pairs of length and width can sum to the same semi-perimeter (6+4=10 and 8+2=10, both giving P=20 cm).
35
Short Answer
Medium
1 Mark
Tariq measures an L-shaped room and calculates perimeter by only adding the 4 longest outer walls, omitting 2 inner corners. Why is this incorrect?
A
Perimeter must include the length of EVERY single segment along the closed boundary
B
Inner corners do not have length
C
L-shapes do not have perimeters
D
Tariq should have multiplied by 6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Perimeter must include the length of EVERY single segment along the closed boundary
Step-by-Step Explanation:
Perimeter requires summing every segment along the boundary without skipping any edges.
36
Short Answer
Medium
1 Mark
A student calculates the perimeter of a 6 cm by 4 cm rectangle as 24 cm. What did the student do wrong?
A
The student multiplied length × width (calculating area = 24 cm²) instead of adding all 4 sides (Perimeter = 20 cm)
B
The student added 6 + 4 only
C
The calculation is correct
D
Perimeter cannot be calculated
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The student multiplied length × width (calculating area = 24 cm²) instead of adding all 4 sides (Perimeter = 20 cm)
Step-by-Step Explanation:
Perimeter is 2 × (6 + 4) = 20 cm. 6 × 4 = 24 cm² is the area.
37
Fill in the Blanks
Medium
1 Mark
A square has a perimeter of 100 cm. What is the length of ONE side?
A
25 cm
B
23 cm
C
29 cm
D
50 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
25 cm
Step-by-Step Explanation:
Side length = 100 ÷ 4 = 25 cm.
38
Fill in the Blanks
Medium
1 Mark
A rectangle has a perimeter of 74 cm. If its length is 25 cm, what is its width?
A
12 cm
B
14 cm
C
11 cm
D
12 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12 cm
Step-by-Step Explanation:
Two lengths = 50 cm. Remaining for 2 widths = 74 - 50 = 24 cm. Width = 12 cm.
39
Short Answer
Medium
1 Mark
A photograph measuring 15 cm by 10 cm is framed with lace ribbon. If lace costs $2 per 10 cm, how much does the lace border cost?
A
$10
B
$8
C
$12
D
$15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$10
Step-by-Step Explanation:
Perimeter = 2 × (15 + 10) = 50 cm. 50 cm ÷ 10 = 5 units. 5 × $2 = $10.
40
Short Answer
Medium
1 Mark
A gardener wants to put wire fencing around a square vegetable patch with side 9 metres. Fencing costs $5 per metre. What will the fencing cost in total?
A
$180
B
$160
C
$200
D
$90
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$180
Step-by-Step Explanation:
Perimeter = 4 × 9 m = 36 m. Cost = 36 × $5 = $180.
41
Short Answer
Medium
1 Mark
At the Art Gallery Picture Frame, an organizer installs a wooden border around the Oil Canvas (25 m long and 12 m wide). What is the total length of border required?
A
74 metres
B
68 metres
C
82 metres
D
300 metres
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
74 metres
Step-by-Step Explanation:
Border length = 2 × (25 + 12) = 74 metres.
42
Multiple Choice
Easy
1 Mark
Which unit is appropriate for measuring perimeter?
A
Centimetres (cm) or metres (m)
B
Square centimetres (cm²)
C
Litres (L)
D
Grams (g)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Centimetres (cm) or metres (m)
Step-by-Step Explanation:
Perimeter is a linear distance, measured in linear units like cm, m, or km.
43
Multiple Choice
Easy
1 Mark
A triangle has sides of 8 cm, 11 cm, and 14 cm. What is its perimeter?
A
33 cm
B
30 cm
C
35 cm
D
32 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
33 cm
Step-by-Step Explanation:
8 + 11 + 14 = 33 cm.
44
Multiple Choice
Easy
1 Mark
What is the perimeter of a square with sides of length 25 cm?
A
100 cm
B
95 cm
C
108 cm
D
625 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
100 cm
Step-by-Step Explanation:
Square perimeter = 4 × 25 = 100 cm.
45
Multiple Choice
Easy
1 Mark
Calculate the perimeter of a rectangle with length 25 cm and width 12 cm:
A
74 cm
B
70 cm
C
80 cm
D
300 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
74 cm
Step-by-Step Explanation:
Perimeter = 2 × (25 + 12) = 2 × 37 = 74 cm.
46
Short Answer
Hard
2 Marks
A rectangular swimming pool is 12 m long and 6 m wide. A 1-metre wide paved walking path surrounds the pool completely on all sides. What is the outer perimeter of the paved path?
A
44 metres
B
36 metres
C
40 metres
D
48 metres
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
44 metres
Step-by-Step Explanation:
Outer length = 12 + 1 + 1 = 14 m. Outer width = 6 + 1 + 1 = 8 m. Outer perimeter = 2 × (14 + 8) = 2 × 22 = 44 metres.
47
Short Answer
Hard
2 Marks
An equilateral triangle and a square have the exact same perimeter of 36 cm. How much longer is a side of the triangle than a side of the square?
A
3 cm longer
B
2 cm longer
C
4 cm longer
D
1 cm longer
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3 cm longer
Step-by-Step Explanation:
Triangle side = 36 ÷ 3 = 12 cm. Square side = 36 ÷ 4 = 9 cm. Difference = 12 - 9 = 3 cm longer.
48
Short Answer
Hard
2 Marks
If you double the side length of a square from 5 cm to 10 cm, what happens to its perimeter?
A
The perimeter exactly doubles from 20 cm to 40 cm
B
The perimeter quadruples to 80 cm
C
The perimeter stays the same
D
The perimeter increases by 5 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The perimeter exactly doubles from 20 cm to 40 cm
Step-by-Step Explanation:
Perimeter = 4 × side. Doubling the side doubles the perimeter: 4 × 5 = 20 cm; 4 × 10 = 40 cm.
49
Short Answer
Hard
2 Marks
Can two completely different rectangles have the exact same perimeter? Explain.
A
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
B
No, each perimeter belongs to only one rectangle
C
Only if both rectangles are squares
D
No, because lengths must match
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes; for example, a 6×4 rectangle and an 8×2 rectangle both have a perimeter of 20 cm
Step-by-Step Explanation:
Different pairs of length and width can sum to the same semi-perimeter (6+4=10 and 8+2=10, both giving P=20 cm).
50
Short Answer
Medium
1 Mark
Tariq measures an L-shaped room and calculates perimeter by only adding the 4 longest outer walls, omitting 2 inner corners. Why is this incorrect?
A
Perimeter must include the length of EVERY single segment along the closed boundary
B
Inner corners do not have length
C
L-shapes do not have perimeters
D
Tariq should have multiplied by 6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Perimeter must include the length of EVERY single segment along the closed boundary
Step-by-Step Explanation:
Perimeter requires summing every segment along the boundary without skipping any edges.